%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET639+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:32:59 AM UTC 2026
% Result : Theorem 10.82s 1.95s
% Output : CNFRefutation 10.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 48 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 14 ~; 12 |; 3 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_intersection,axiom,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(prove_th121,conjecture,
! [X0,X1] :
( ( intersection(X1,X0) = 'empty$uset'
& subset(X0,X1) )
=> X0 = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( intersection(X1,X0) = 'empty$uset'
& subset(X0,X1) )
=> X0 = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[prove_th121]) ).
cnf(c0,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_intersection]) ).
cnf(c1,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c3,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c4,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c6,plain,
( member(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c11,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c21,plain,
subset(sK22,sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
intersection(sK23,sK22) = 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c23,plain,
sK22 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
intersection(sK22,sK23) = sK22,
inference(resolution,[status(thm)],[c0,c21]) ).
cnf(d1,plain,
( member(X0,sK23)
| ~ member(X0,sK22) ),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( member(sK9(sK22,X0),sK23)
| subset(sK22,X0) ),
inference(resolution,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
( ~ member(X0,sK23)
| ~ member(X0,sK22)
| member(X0,'empty$uset') ),
inference(superposition,[status(thm)],[c22,c4]) ).
cnf(d4,plain,
( ~ member(X0,sK23)
| ~ member(X0,sK22) ),
inference(resolution,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
( subset(sK22,X0)
| ~ member(sK9(sK22,X0),sK22) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( subset(sK22,X0)
| subset(sK22,X0) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
intersection(sK22,X0) = sK22,
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
intersection(sK22,sK23) = 'empty$uset',
inference(demodulation,[status(thm)],[c22,c11]) ).
cnf(d9,plain,
sK22 = 'empty$uset',
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c23,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET639+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n006.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Sat Sep 26 08:01:56 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/1.95 % SZS status Theorem for theBenchmark.p
% 10.82/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------